1. Field of the Invention
The present invention generally relates to a method, system and software product used in the area of mechanical computer-aided engineering design and analysis, more particularly to efficient simulation of manufacturing process of shapeable material using finite element analysis.
2. Description of the Related Art
Finite element analysis (FEA) is a computerized method widely used in industry to model and solve engineering problems relating to complex systems such as three-dimensional non-linear structural design and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. With the advent of the modern digital computer, FEA has been implemented as FEA software. Basically, the FEA software is provided with a model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the system under analysis is represented by solids, shells and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The model is comprised of a finite number of elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA software then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermo-conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, etc.) are specified. In this fashion a model of the object and its environment is created.
As the finite element method progressed in the past decades, not only manufactured products can be analyzed, manufacturing processes can also be simulated. For example, a diaper manufacturer would be more competitive with a more efficient manufacturing process to reduce the costs. Physical creation of a prototype manufacturing process is generally expensive and impractical, thereby a computer simulation of manufacturing process of shapeable material (e.g., paper, fabric, sheet metal, etc.) using FEA is used heavily for the manufacturer to improve the manufacturing process.
Using the diaper manufacturing process as an example, continuous shapeable materials (i.e., paper, fabric) are fed into a machine through a number of rollers. As depicted in FIG. 2A, a very simple machinery with shapeable material is illustrated. The portion of the material between rollers C and D, or E and F is of interest for the design engineer of a particular manufacturing process. In order to obtain the detailed steady state behavior of the shapeable material (e.g., FIG. 2B), not only a very fine thus large FEA mesh is required, but a sufficiently long enough time must be simulated. As a result, very large computation resource is needed to simulate a particular scenario. A design engineer usually wishes to simulate a number of scenarios (e.g., what-if study) to study the trade-offs. The large computation requirement may be solved with large number of parallel processors as described below.
One of the means to increase computing efficiency is to use parallel processing/computing in the recent years. The parallel computing has progressed such that many of the finite element analyses are performed using more than one processors (i.e., CPU). Some of the FEA are performed with a high number of the processors (e.g., 32, 64, 128 processors or more). However, in order to ensure computing efficiency, it is critical that the computation loads be balanced. Otherwise, the benefit of additional processors cannot be realized at all. When executing a FEA in a parallel computing server, a technique referred to as domain decomposition is used for load balancing, which can help achieving high computation efficiency.
When domain decomposition and other load balancing techniques are included in a FEA for simulating a manufacturing process of shapeable materials, there is an additional challenge. In applying the domain decomposition, which is done at the beginning of the simulation, a subset of elements is distributed to each processor. When the shapeable materials are fed into the machinery continuously, and only certain portions of the shapeable materials are of interest, an efficient simulation using FEA requires activating elements at the input and deactivating elements at the output. However, inactive elements would destroy the load balancing since the processors where these elements reside do not have work to do hence idle. It is therefore desirable to have an efficient new method to simulate a manufacturing process of shapeable materials using finite element analysis in a parallel computing server where all processors contain nearly equal numbers of active elements and a small number of inactive elements.